3 Answers
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Normally, in industry, you combine the butter and flour, and cook it for a bit (usually gets a nice nutty aroma). Then, you heat the milk to a boil, and add some of the milk to the cooked roux (fat and flour). This will be VERY thick. You can easily whisk the lumps out of that. You then add this back into the other milk, which thickens the milk. Also, in industry, there is often just a big pail of roux, and a shortcut is to heat the milk, and then add the roux in a bit at a time, whisking like hell to get out the lumps. You can control the thickness of the sauce better that way. When you have the desired thickness, you then season.

I was taught to always add cold roux to hot stock/milk, or cold stock to hot roux in order to prevent lumps, and my culinary arts textbook (On Cooking, 4th Edition) confirms this. It is also possible you did not cook the roux long enough before adding milk; after a minute or two with whisking, it should be bubbling and pasty in texture, with no visible clumps. This texture means the fat and flour are fully incorporated, reducing clumping.

I cook the butter and the flour together for a bit, like mrwienerdog said, until its a very dense mass. The trick to avoid lumps is to then add the milk (I don't heat it, like BobMcGee said) very little by little.

I've found that adding a lot of milk will leave undisolved clumps of roux, but if you add a tiny bit of milk and mix it in, you'll get a slightly lighter roux, to which you can add another tiny bit of milk, and so on. All the while mixing vigorously over medium low heat. Once it has the right texture/consistency add the seasoning. Remember that once it cools béchamel will be (much) more thick than what it seems when your making it (don't over do it or it'll be solid).